Matrix Completion with Sparse Noisy Rows

TL;DR

This paper introduces an interactive algorithm for exact low-rank matrix completion that is robust to sparse, noisy rows, expanding the understanding of matrix recovery under row-wise noise models.

Contribution

It proposes a novel row-wise noise model and an algorithm that guarantees recovery of the underlying matrix under this condition.

Findings

The algorithm successfully recovers matrices with noisy rows.

The paper establishes conditions for recoverability under row-wise noise.

Experimental results demonstrate robustness to noise in practical scenarios.

Abstract

Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has been previously studied by many researchers under given condition that the noise is sparse and existing in some of the columns. In this paper, we assume that each row can receive random noise instead of columns and propose an interactive algorithm that is robust to this noise. We show that we use a parametrization technique to give a condition when the underlying matrix could be recoverable and suggest an algorithm which recovers the underlying matrix.